Coincident structural and magnetic order in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ revealed by high-resolution neutron diffraction

We present neutron diffraction analysis of ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ over a wide temperature (10 to 300 K) and compositional $\left(0.11\le x\le 0.79\right)$ range, including the normal state, the magnetically ordered state, and the superconducting state. The paramagnetic to spin-density wave and orthorhombic to tetragonal transitions are first order and coincident within the sensitivity of our measurements ($\sim 0.5$ K). Extrapolation of the orthorhombic order parameter down to zero suggests that structural quantum criticality cannot exist at compositions higher than $x=0.28$, which is much lower than values determined using other methods, but in good agreement with our observations of the actual phase stability range. The onset of spin-density wave order shows a stronger structural anomaly than the charge-doped system in the form of an enhancement of the $c/a$ ratio below the transition.

Figure 1

Normalized magnetization measurements on representative samples. Superconducting volume fractions are estimated using the magnitude of the diamagnetic response and are $\ge 80\%$ for all samples.

Figure 2

(a) Depiction of the crystal structure of $\text{Ba}{\mathrm{Fe}}_2{\mathrm{As}}_2$. (b) Basal plane lattice vectors and Fe sublattice of the $I4/mmm$ cell viewed along the (001) direction. (c) $Fmmm$ cell in the same view. The symmetry breaks when $\gamma$ diverges from 90°, though primitive $a$ and $b$ axes remain the same which gives a conventional orthorhombic cell. The magnitude of the distortion is exaggerated for clarity.

Figure 3

(a) Normalized lattice parameters as a function of composition at 300 K. The ${\mathrm{Ba}\mathrm{Fe}}_2{\mathrm{As}}_2$ point is taken from Ref. [26] and the ${\mathrm{BaFe}}_2{\mathrm{P}}_2$ point is taken from Ref. [27]. (b) $T$ dependence of $c$ axis of $x=0.115$ (top panel) and $x=$ 0.19, 0.205, 0.24, and 0.25 (bottom panel). The inset shows the temperature dependence of (004) reflection peak position. (c) Dependence of $a_{\mathrm{orth}}$ and $b_{\mathrm{orth}}$ axes as a function of temperature. For the tetragonal data points, $a$ is scaled by a factor of $\sqrt{2}$ in order to compare equivalent lattice vectors. (d) Volume of $x=0.115$ as a function of temperature. In order to avoid artificial discontinuities when changing from one model to the other, only orthorhombic refinements are used for all temperatures. The volume is given in the body-centered cell by scaling by 0.5. (e) The orthorhombic order parameter is shown for $x=0.115$, 0.205, 0.24, and 0.25.

Figure 4

Histograms of the $x=0.115$ (upper panel) and 0.205 (lower panel) POWGEN data at selected temperatures. Arrows point to the magnetic peaks in the 10 K scans.

Figure 5

The refined magnetic moments for $x=0.115$ and 0.205 from the Rietveld refinements are shown in the upper panel. The lower panel shows an overlay of the integrated intensities of the (103) magnetic reflection from the HB-1A experiment (closed red circles) and the refined orthorhombic order parameter (open blue circles).

Figure 6

(a) The phase diagram of ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$. Phase lines are drawn to guide the eye. Error bars for both axes are contained within the symbols. (b) Composition dependence of the orthorhombic order parameter prefactor $A_{\mathrm{s}}$ (blue), and the 10 K refined magnetic moment (red).

Figure 7

Normalized lattice parameters as a function of temperature of (a) ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ and (b) ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ $(x=0$, 0.1, 0.15, and 0.24). The upper panels show the $a_{\mathrm{tet}}$ normalized to each composition's room temperature value, and the lower panels show $c/a$ ratios normalized in the same manner. The data points for $x=0$ and the K-substituted compounds is taken from Ref. [26]. The lines are guides to the eye.